how do i can solve a trigonometric equation which is restricted arguments?

#1 Posted: 7/4/2021 11:50:31 PM

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Hi
i want to solve an equation about adding three cosine term which are constrained:

cos(2 pi(x+y-2z))+cos(2 pi(y+z-2x))+cos(2 pi(z+x-2y))=0

with constraint 0
can some one please guide me?

i wrote this command but it did not work:

solve({cos(2*Pi*(x+y-2*z))+cos(2*Pi*(y+z-2*x))+cos(2*Pi*(z+x-2*y)) = 0, 0 <= x, x <= 1, y <= 1, z <= 1, x < y, y < z}, [x, y, z], explicit)
when we write this command as this:
solve({cos(2*Pi*(x+y-2*z))+cos(2*Pi*(y+z-2*x))+cos(2*Pi*(z+x-2*y)) = 0,[x, y, z], explicit)
i do not see any change in the figures
apparently my restriction do not work!
whats the problem?
someone told me i should solve this problem with Draghilev method because this problem should solve with numerical method

#2 Posted: 7/5/2021 10:41:14 AM

overlord

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More experienced users may help you better than me.
But your equation seems to have infinite solutions.

Regards

al_nleqsolve equ(x,y,z).sm (10 KiB) downloaded 27 time(s).

#3 Posted: 7/5/2021 6:20:46 PM

Alvaro Diaz Falconi

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As overlord points, there are infinite solutions. Just like the better visual representation for z = f(x,y) is a surface in the 3D space, w = f(x,y,z) is a hypersurface in the 4D space. But we can't see that plot. So, here a plot of families of that 4D hypersurface, like a contour plot, but with surfaces.

About Dragilev method, I can't find my setup for 3D, and the expert there is Viacheslav (uni).

Plots4D.sm (111 KiB) downloaded 33 time(s).
Plots4D.pdf (393 KiB) downloaded 44 time(s).

Best regards.
Alvaro.

1 users liked this post

Oscar Campo 7/5/2021 9:01:00 PM

#4 Posted: 7/5/2021 9:15:59 PM

Jean Giraud

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#5 Posted: 7/6/2021 1:46:40 AM

Fridel Selitsky

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One of the solutions by the Draghilev method.

Draghilev.sm (23 KiB) downloaded 27 time(s).

1 users liked this post

Alvaro Diaz Falconi 7/6/2021 3:06:00 AM

#6 Posted: 7/6/2021 3:05:22 AM

Alvaro Diaz Falconi

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Well, Fridel it's an expert too, thanks.

Joining above Dragilev and 4D methods.

Plots4D_DM3.sm (111 KiB) downloaded 40 time(s).
Plots4D_DM3.pdf (182 KiB) downloaded 38 time(s).

Best regards.
Alvaro.

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Fridel Selitsky 7/6/2021 3:50:00 AM

#7 Posted: 7/6/2021 12:19:07 PM

Fridel Selitsky

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Discussion of this problem on the maple forum featuring
the author of this question(rahmati)
https://www.mapleprimes.com/questions/232488-How-Do-I-Can-Solve-A-Trigonometric-Equation

SMath

how do i can solve a trigonometric equation which is restricted arguments?

how do i can solve a trigonometric equation which is restricted arguments? - maple software - Messages

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how do i can solve a trigonometric equation which is restricted arguments? - maple software - Messages